PSI - Issue 13

Mohamed Seghier et al. / Procedia Structural Integrity 13 (2018) 1670–1675 Author name / Structural Integrity Procedia 00 (2018) 000–000

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The M5Tree is calibrated based on the data of the experimental corroded pipes which is made by X60 which are extracted from reference [2]. This data include 28 full-scale experimental burst data point that the mid-strength X60 steel grade varied from 73 to 720 mm for diameter, 3-14.8mm for wall-thickness, 430 - 478MPa for yield strength, 620.9 – 673.5MPa for ultimate strength, 1.5 – 10.5mm for the maximum corroded depth and 25.5-1016 mm for length of corrosion defects with corroded burst test ranged between 7.55 and 36.33MPa. 1.1.2 Monte Carlo simulation The Monte Carlo method is the most straightforward method used in the reliability of corroded pipelines. Basically the simulation is based on the generation of a large number of random variables used in the limit state function calculation, then the failure probability is expressed using the following expression: � � 1 � ��� ����� � �� �� � � ��� (2) where, represent an indicator equal to 1 if the statement is true or 0 otherwise, is the number of the failure scenarios, while is the total number of simulations. The convergence condition taken in this study to attend sufficient precision is the variation coefficient, this latter should satisfy the following condition: ��� � � �1 � � � � � � 1� � ���� (3) where, CoV is the variation coefficient, and � is the failure probability provided by the MC technique. 1.1.3 M5 tree model algorithm with Monte Carlo The M5Tree model is used for approximating the performance function of the corroded pipes under burst pressure failure mode. The ten million random sample data points-based MCS is applied for the evaluating the LSF to approximate the failure probability in the next process. The failure probability by hybrid M5Tree and MCS can be approximated by the following steps: Step 1: Define initial parameters Step 3: Generate N random samples –based MCS using statistical properties of random variables Step 4: Approximate the performance function for N- random samples using M5Tree model Step 5: Approximate the failure probability using M5Tree based on the predicted values of performance function for burst pressure of corroded pipe in Step 4 . 2. Case of Study To show the robust and the applicability of the proposed method (M5tree model combined with Monte Carlo Simulation) a candidate gas pipeline carries made from medium grade steel, X60. The pipe is 40 inches in diameter, was inspected to determine the corrosion defects on pipe-wall-thickness, 100 km was the inspected part of the pipe which reveal a huge number of defects. A statistical analysis of corrosion defects in the external wall of the pipeline was carried out using the Anderson Darling test for the purpose of finding the best fitting distortion of the input parameters based on the inspection data. The chosen distribution are Normal, Log-Normal, Weibull, Frechet and Gumbel distributions while the tested variables are the length and the depth of corrosion defects. The diameter and wall thickness distribution were taken as the nominal values with a slightly CoV. The operating pressure is characterized by a Gumbel distribution. Table 1 presents the input variables used in the reliability analysis. 1- Sample points to calibrate the M5Tree model, number of random samples in MCS ( N ). 2- Give statistical properties of random variables ( μ and  ) and their distributions. Step 2: Generate the performance function by using M5Tree model.